Erik Bølviken

Seasonality, density dependence, and population cycles in Hokkaido voles

Voles and lemmings show extensive variation in population dynamics regulated across and within species. In an attempt to develop and test generic hypotheses explaining these differences, we studied 84 populations of the gray-sided vole (Clethrionomys rufocanus) in Hokkaido, Japan. We show that these populations are limited by a combination of density-independent factors (such as climate) and density-dependent processes (such as specialist predators). We show that density-dependent regulation primarily occurs in winter months, so that populations experiencing longer winters tend to have a stronger delayed density-dependence and, as a result, exhibit regular density cycles. Altogether, we demonstrate that seasonality plays a key role in determining whether a vole population is cyclic or not.

Blind deconvolution of ultrasonic traces accounting for pulse variance

The ability of pulse-echo measurements to resolve closely spaced reflectors is limited by the duration of the ultrasonic pulse. Resolution can be improved by deconvolution, but this often fails because frequency selective attenuation introduces unknown changes in the pulse shape. In this paper we propose a maximum a posteriori algorithm for simultaneous estimation of a time varying pulse and high-resolution deconvolution. A priori information is introduced to encourage estimates where the pulse varies only slowly and the reflectivity sequence is sparse. This adds sufficient regularization to the problem, and no further assumptions on the pulse such as minimum phase or a particular parametric form are needed. The joint pulse and reflectivity estimate are computed iteratively by alternating steps of pulse estimation and reflectivity estimation. The first step amounts to only a linear least squares fit. The second step is a difficult combinatorial optimization problem that we solve by a suboptimal but efficient search procedure. Due to the sparseness assumption, our approach is particularly suited for layered media containing a limited number of abrupt impedance changes. This is a situation of interest in many applications of nondestructive evaluation. Synthetic and real data results show that the algorithm works well.

Monte Carlo filters for non-linear state estimation

It is shown through a simple mathematical formula that Monte Carlo computations of Bayesian filter estimates do not demand many repetitions. A general algorithm is constructed, and its performance on difficult problems demonstrated.

Confidence Intervals from Monte Carlo Tests

Abstract Monte Carlo tests have exact level when the distribution of the test statistic is free of nuisance parameters. Confidence sets obtained by inverting such tests are also exact but may have a complicated structure. The sets reduce to intervals if the sampling can be organized in a special way. A sufficient condition is that the test statistic is monotone in the parameter of interest when all random drawings are kept fixed. Examples given include models from the one-parameter exponential class. A simple theory quantifying the impact of Monte Carlo uncertainty is also developed.

Relaxation using models from quantum mechanics

Abstract We make an analogy between a single pixel and its first-order neighbours in an image and single particle models from quantum physics. The analogy is created by identifying the observed grey levels and the noise variance with the potential function and the energy of the physical system. The approach is used to set up novel and strongly data-dependent local weights in relaxation schemes. Both image restoration and segmentation are considered. The new methods competed favourably with the Besag ICM and Rosenfeld relaxation on several simulated and real images.

Deterministic and Stochastic Particle Filters in State-Space Models

Optimal or Bayesian filtering in state-space models is a question of computing series of linked numerical integrals where output from one is input to the other (Bucy and Senne 1971). Particle filtering can be regarded as comprising techniques for solving these integrals by replacing the complicated posterior densities involved by discrete approximations, based on particles (Kitagawa 1996). There is evidence that the numerical errors as the process is iterated often stabilise, or at least do not accumulate sharply (see section 5.2.5). Filters of this type can be constructed in many ways. Most of the contributions to this volume employ Monte Carlo designs (see also (Doucet 1998) and the references therein). Particles are then random drawings of state vectors under the current posterior. This amounts to Monte Carlo evaluations of integrals. Numerically inaccurate, but often practical and easy to implement, general methods to run the sampling have been developed. Alternatively, particles can be laid out through a deterministic plan, using more sophisticated and more accurate numerical integration techniques. Such an approach has been discussed in (Kitagawa 1987), (Pole and West 1988) and (Pole and West 1990), but recently most work has been based on Monte Carlo methods. To some extent, Monte Carlo and deterministic particle filters are complementary approaches, and one may also wonder whether they may be usefully combined (see (Monahan and Genz 1997) for such a combination in a non-dynamic setting). Emphasis in this paper is on deterministic filtering. A general framework can be found in the above-mentioned references and in (West and Harrison 1997)[Section 13.5]. We shall present a common perspective in the next section, where our contribution will be on design issues.

Automated prediction of sedimentary facies from wireline logs

Abstract The problem addressed is whether a computer can be programmed to identify depositional facies from a set of wireline logs. The basic approach is to let the computer learn by itself the patterns to search for by feeding it log signatures that have already been assigned facies labels. Having gone through this training phase, it can make sedimentary predictions from new data. The underlying model is a mathematical formalization of the idea that sedimentary processes have deposited lithological sequences which influence the observed log traces. Stochastic descriptions are used for these relationships. Markov chains link the lithology to the underlying sedimentary facies. The upward transition probabilities of the Markov chain are the main features which discriminate sedimentary facies. An efficient reconstruction algorithm permits probabilistic restoration of both lithology and sedimentology. This allows the uncertainty of the conclusions to be quantified, and more than one interpretation can be put forward where appropriate. Results of the tests are promising.

Computer studies of the evolution of planetary and satellite systems I. Description of the program: Preliminary tests

In this paper we describe a CDC-Cyber 74 program for computer simulation of the evolution of a system consisting of a large number of objects in orbit around a central body or primary. Some preliminary tests done with the program will also be described.

Arson, statistics and the law: can the defendant's proximity to a large number of fires be explained by chance?

The statistical evidence which played a major part in a case of arson in Norway is presented as a case study. A fireman was known to have been present at the scenes of fire in the hours prior to their onset in no less than 24 out of 37 cases of forest fire. The study, through probabilistic analysis, attempts to throw light on whether this was so strikingly often that he had to be the arsonist, carefully taking into account special features that could explain the peculiar behaviour of the defendant. The conclusion hinged on certain input parameters to the calculation, and the principal aim of the work was to organize, structure and reduce the material to a few quantities that were easier to comprehend than the problem in its original form. The court accepted the relevance of the calculations, and used it against the defendant, but he was still acquitted. A number of issues related to probabilistic interpretation of evidence are discussed.

Non-linear state estimation by Monte Carlo filters: a six-dimensional example

We present a general Monte Carlo-based algorithm for computing Bayesian estimates in non-linear state space models, and apply it to bearings-only target tracking. The parameters of the measurement noise are determined online as part of the state estimation. The state vector then becomes six-dimensional, but the problem is still handled in real time.